ANOVA: Notes on Understanding
Interaction

Last updated:
27 Apr 2005

Some notes that might help
in grasping
ANOVA interactions:

Interaction means that the
IVs are not independent. The IVs have a complex (interactive)
influence on the DV.

An interaction means that the main effects can
not
be relied upon to tell the full story. When there is an
interaction effect, it means the main effects do not collectively
explain all of the influence
of the IVs on the DV. The IVs have an interactive effect on the DV,
which means the cell means must be examined for
each sub-group -- this is where the nature / direction of the
interaction can be found.

Interaction in ANOVA
is
equivalent to interaction in MLR.

Understanding of interaction can be pursued
mathematically or it be grasped graphically. It is easiest to
depict using a 2x2 factorial, mixed or within-subjects design. Interaction is indicated by non-parallel lines
in a line graph.
In other words, if the lines are crossed or would eventually
cross if extended, then there is an interaction. Of course the
lines are rarely perfectly parallel, so the real question is
about whether the different pattern of means across the sub-groups is
to be considered unlikely to have occurred by chance.
The significance test of the interaction and its associated effect size
are the key pieces of information. The figure below shows some possible outcomes of the
experiment investigating the effects of intensity of exercise and time
of day on amount of sleep.

Make when interpreting interaction to describe the direction
of any relationships.